1. Field of the Invention
This invention relates in general to vertical-scanning interferometry (VSI) for surface characterization. In particular, it relates to a statistical approach applied to determine the fringe order of phase data for measuring uniform micro-features in a sample, such as in patterned sapphire substrates (PSSs) of light emitting diodes (LEDs).
2. Description of the Related Art
The high-brightness LED (HB-LED) industry is experiencing rapid growth as a result of demand for applications in televisions and computer displays, automotive lighting, mobile-phone and other hand-held device displays, and as a more efficient solution for general residential and commercial lighting. Each of these applications requires end products that exhibit tightly controlled efficiency and color, with center wavelength variation of no more than 4 nanometers, so as to be undetectable by the human eye. Optical interferometric profilometry is a proven method for measuring and monitoring HB-LED wafer surfaces rapidly and repeatably in three-dimensional (3D) detail, thereby enabling an increase in production efficiency and quality.
The structure of a typical LED includes gallium nitride (GaN) n-p layers interlaced with multi-quantum well (MQW) layers grown epitaxially on a sapphire substrate S, as shown in FIG. 1(a). A transparent protective layer of conductive indium tin oxide (ITO) completes the LED structure. Usually, only a relatively small percentage of the total light emitted by the LED can be extracted due to the large difference in the index of refraction between the GaN (and the other LED materials) and air. This difference produces total internal reflection at the device-air interface and light is therefore reflected back and lost into the device. In order to enhance the efficiency of light extraction, several methods are currently used in the art, including random surface texturing, flip-chip technology, photonic crystals, and patterned sapphire substrates.
PSS structures, illustrated in FIG. 1(b), have a surface patterned with uniform, dome-like, features D that protrude from the flat base B of the surface. These 3-D features have several advantages over the other approaches for improving LED performance and are, therefore, widely used in commercial HB-LED devices. Only standard semiconductor photolithographic processes are required to create PSS structures, which reduces the cost of implementation. Also, in addition to enhancing light extraction efficiency, PSS structures reduce dislocation defect density, both of which contribute significantly to overall device efficiency. Thus, manufacturers utilize a variety of PSS structure shapes to enhance LED performance and light extraction.
The exact shape of PSS structures varies from manufacturer to manufacturer, with typical patterns including pyramidal, conical, or hemispherical shapes. Each individual protrusion is typically several micrometers in width and between 1 and 2 micrometers in height, with an overall pattern pitch between 2 and 5 micrometers. The shape is optimized during the development phase of the structure, while in production manufacturers work to control the width, height and pitch at a high sampling rate for process control. The height of the PSS structures is particularly crucial because deviations from the target value affects efficiency and wavelength uniformity, and can even cause electrical shorts if the features penetrate the active layer. Also, because the deposition process is very slow, maintaining height uniformity is very important for production throughput.
Scanning electron microscopes (SEMs) are normally used to image PSS structures during the research and development phase of a product and to visualize the fine details of the sidewall shape. Atomic force microscopes (AFMs) are popular as well, both for research and for process control, because they allow non-destructive sample handling and high-resolution imaging. Where sampling rates are such that throughput is not a factor, these technologies provide true 3D quantification of features, including sub-nanometer vertical resolution and very high slope capability. However, LED manufacturers process hundreds to thousands of PSS substrates daily and their throughput requires fast, accurate, and non-destructive 3D surface metrology, which is not compatible with either SEM or AFM utilization.
For rapid feedback on production-line applications, white-light interferometry (WLI) is quickly becoming the technology of choice. White light interferometry (an optical interferometric profilometry technique) has been employed with great success in high-volume production environments for more than two decades, providing 3D surface maps with nanometer-level accuracy and repeatability. As is well understood in the art, a light beam from a broadband light source is split into two by a beam splitter, with one beam directed to a high-quality reference surface and the other to the sample surface. After reflection from their respective surfaces, these two beams are recombined at an optical detector, usually a CCD camera, and the difference in the length of the paths followed by each beam produces a sinusoidal interference signal when the difference in the path lengths of the two beams is near zero. As the objective scans through focus in the vertical direction, each point on the measured surface passes through this equal-path location and the signal has maximum contrast. The vertical scan location of the maximum contrast point corresponds to the surface height for each pixel in the image, thereby producing an accurate 3D map of the surface.
The accuracy of WLI has been improved over the years by combining phase-shifting interferometry (PSI) techniques with conventional white-light vertical scanning. Such approaches have enabled measurements of steep or discontinuous surfaces without 2π ambiguity and with PSI resolution. For example, U.S. Pat. No. 7,605,925, hereby incorporated by reference in its entirety, describes performing a broadband interferometric vertical scan of a sample surface to produce interference data and a corresponding coarse surface profile in real time using a conventional technique, such as a center-of-mass calculation. A fine surface map is obtained concurrently using a quadrature-demodulation algorithm applied in real time to the same interference data used for the coarse surface calculation. The fine surface map is then combined with the coarse surface profile using an unwrapping technique that produces a final surface map with sub-nanometer resolution within a large height range. This technique has been referred to as high definition vertical scan interferometry (HDVSI).
However, in practice scanner steps are not exactly constant and cannot be determined precisely by calibration. To improve this shortcoming, U.S. Pat. No. 7,898,672, hereby also incorporated by reference in its entirety, teaches an error correction procedure for scanner position wherein the filter parameters of the quadrature demodulation module of the HDVSI algorithm are adjusted using a reference signal from an independent position measurement device (PMD). As illustrated in the diagram of FIG. 2, the step size generated by the PMD at each scanner step is substituted for the nominal scanner step in the quadrature demodulation algorithm calculating phase and in the coherent envelope algorithm calculating peak. This substitution eliminates all errors produced by scanner nonlinearities. Furthermore, over the large number of steps carried out during a normal scanning range, random scanner-position errors (such as produced by vibration and other system noise) are automatically corrected by integration over their normal distribution around the noise-free position value. Therefore, a complete correction of scanner-position error is achieved using the reference signal.
However, as one skilled in the art will readily appreciate, the width and especially the height measurements of the typical PSS feature, as well as similar structures in other surfaces, present a particularly difficult challenge because of the very steep walls in the transition zone from the base of the sapphire substrate to the patterned feature. In such zone the broadband light is largely scattered, yielding very little contrast for meaningful white-light interferometry, with a signal that often is indistinguishable from background and other noise. For example, FIG. 3 illustrates in cross-section the results of a conventional VSI measurement of a patterned sapphire structure with dome-like features about 3.50 nm wide and 1.54 nm high (based on AFM measurements). It is difficult to determine the width of the feature by identifying the location where the base is projected upward (and vice versa on the other side of the feature). The approximately true profile of the dome features is illustrated by the phantom lines D and the true base line of the sapphire structure by the solid line B. The VSI line illustrates the “batwing” artifacts produced both at the top of each dome (because of the change in slope) and in the transition zones (because of the steep slope) by conventional vertical scanning. It is clear that the measurement does not produce a precise estimate of width and height. The main problem with the data near the peaks of the domes lies in the fact that the phase data utilized to generate the map are often subject to fringe-order errors that appear randomly in pixel-by-pixel analysis.
A not much better result is achieved using the HDVSI technique of FIG. 2. As seen in FIG. 4, this improved procedure still produces batwing artifacts and fringe errors (i.e., errors resulting from 2 π ambiguity) that make it impossible to calculate precise dimensions for the patterned features on the sapphire substrate. The same problem of random fringe-order error produces batwings in the pixel-by-pixel procedure used to generate PSS height maps. Therefore, in order to enable fast and reliable measurements of such features in PSSs and similar structures for quality control in a production environment, there is still a need for an improved technique. The present invention describes an optical profilometric solution based on the general idea of combining the best available height data for the substrate with phase data for the relatively smooth area around the tops of the features using a statistical approach to determine the correct fringe order of the phase data. The invention is illustrated with data produced by the HDVSI algorithm of FIG. 2 with sample features having the structure of PSSs, but it is understood that the invention is more broad in its scope and that it can be applied to interferometric data obtained by any measurement technique, so long as a good phase map is available for the tops of the features and a reliable height map for the entire surface of the substrate is available for producing a fringe-order map. Such maps could be obtained, for example, by measuring the substrate with dual-wavelength interferometry, or by a combination of VSI and PSI measurements.